In order to be able to control electromagnetic devices with exact timing to the greatest possible extent, short response times and short release times are required. The response times are kept short as a rule by applying an elevated voltage to the electromagnetic device at the onset of an actuation signal. Short release or de-excitation time can be attained with a reversal of the actuation voltage, so that the smallest possible time constant is attained for the exponential response function which is a natural property of the device. If the electromagnetic device is intended to be excited for a controllable duration longer than the duration of the actual actuation signal, then the free-running circuit of the electromagnetic device can be controlled by varying a variable resistor in this free-running circuit as disclosed in the German laid-open application 20 36 655. In this known device for controlling the excitation time of the electromagnetic device beyond the duration of the input signal, however, exact times cannot be attained because of the non-linear current decrease of the electrical current flowing through the device.